Question

An object A is placed on the principal axis of a convex mirror at a distance of 60 cm in front of it. A plane mirror is inserted between the object and the convex mirror at a distance of 40 cm from the object with the reflecting surface of the plane mirror facing the object. If the images formed by the two mirrors coincide, find the focal length of the convex mirror.

• A. 15 cm
• B. 25 cm
• C. 20 cm
• D. 30 cm

Answer 1

Answer: (D)

30 cm

$u=v$ for plane mirror $=40cm$

$v=20cm$ for convex mirror as well since the images coincide and distance between the two mirrors is $20cm$.

$u$ for convex mirror $=-60cm$ (since it is left of the mirror)

From lens formula, $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}=-\frac{1}{60}+\frac{1}{20}$

$\frac{1}{f}=\frac{2}{60}$

$f=30cm$